source: trunk/GSASIIobj.py @ 1790

Last change on this file since 1790 was 1790, checked in by vondreele, 8 years ago

remove unused FORPI from G2strMath
New fitTexture routine to use seq refinement results - seem ok, but needs checking
bring DefaultControls? up to date in G2obj

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  • Property svn:keywords set to Date Author Revision URL Id
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1# -*- coding: utf-8 -*-
2#GSASIIobj - data objects for GSAS-II
3########### SVN repository information ###################
4# $Date: 2015-04-15 21:20:11 +0000 (Wed, 15 Apr 2015) $
5# $Author: vondreele $
6# $Revision: 1790 $
7# $URL: trunk/GSASIIobj.py $
8# $Id: GSASIIobj.py 1790 2015-04-15 21:20:11Z vondreele $
9########### SVN repository information ###################
10
11'''
12*GSASIIobj: Data objects*
13=========================
14
15This module defines and/or documents the data structures used in GSAS-II, as well
16as provides misc. support routines.
17
18Constraints Tree Item
19----------------------
20
21.. _Constraints_table:
22
23.. index::
24   single: Constraints object description
25   single: Data object descriptions; Constraints
26
27Constraints are stored in a dict, separated into groups.
28Note that parameter are named in the following pattern,
29p:h:<var>:n, where p is the phase number, h is the histogram number
30<var> is a variable name and n is the parameter number.
31If a parameter does not depend on a histogram or phase or is unnumbered, that
32number is omitted.
33Note that the contents of each dict item is a List where each element in the
34list is a :ref:`constraint definition objects <Constraint_definitions_table>`.
35The constraints in this form are converted in
36:func:`GSASIIstrIO.ProcessConstraints` to the form used in :mod:`GSASIImapvars`
37
38The keys in the Constraints dict are:
39
40.. tabularcolumns:: |l|p{4.5in}|
41
42==========  ====================================================
43  key         explanation
44==========  ====================================================
45Hist        This specifies a list of constraints on
46            histogram-related parameters,
47            which will be of form :h:<var>:n.
48HAP         This specifies a list of constraints on parameters
49            that are defined for every histogram in each phase
50            and are of form p:h:<var>:n.           
51Phase       This specifies a list of constraints on phase
52            parameters,
53            which will be of form p::<var>:n.
54Global      This specifies a list of constraints on parameters
55            that are not tied to a histogram or phase and
56            are of form ::<var>:n
57==========  ====================================================
58
59.. _Constraint_definitions_table:
60
61.. index::
62   single: Constraint definition object description
63   single: Data object descriptions; Constraint Definition
64
65Each constraint is defined as an item in a list. Each constraint is of form::
66
67[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]
68
69Where the variable pair list item containing two values [<mult>, <var>], where:
70
71  * <mult> is a multiplier for the constraint (float)
72  * <var> a :class:`G2VarObj` object (previously a str variable name of form
73      'p:h:name[:at]')
74
75Note that the last three items in the list play a special role:
76
77 * <fixedval> is the fixed value for a `constant equation` (``constype=c``)
78   constraint or is None. For a `New variable` (``constype=f``) constraint,
79   a variable name can be specified as a str (used for externally
80   generated constraints)
81 * <varyflag> is True or False for `New variable` (``constype=f``) constraints
82   or is None. This will be implemented in the future to indicate if these variables
83   should be refined.
84 * <constype> is one of four letters, 'e', 'c', 'h', 'f' that determines the type of constraint:
85
86    * 'e' defines a set of equivalent variables. Only the first variable is refined (if the
87      appropriate refine flag is set) and and all other equivalent variables in the list
88      are generated from that variable, using the appropriate multipliers.
89    * 'c' defines a constraint equation of form,
90      :math:`m_1 \\times var_1 + m_2 \\times var_2 + ... = c`
91    * 'h' defines a variable to hold (not vary). Any variable on this list is not varied,
92      even if its refinement flag is set. Only one [mult,var] pair is allowed in a hold
93      constraint and the mult value is ignored.
94      This is of particular value when needing to hold one or more variables where a
95      single flag controls a set of variables such as, coordinates,
96      the reciprocal metric tensor or anisotropic displacement parameter.
97    * 'f' defines a new variable (function) according to relationship
98      :math:`newvar = m_1 \\times var_1 + m_2 \\times var_2 + ...`
99
100Covariance Tree Item
101--------------------
102
103.. _Covariance_table:
104
105.. index::
106   single: Covariance description
107   single: Data object descriptions; Covariance
108
109The Covariance tree item has results from the last least-squares run. They
110are stored in a dict with these keys:
111
112.. tabularcolumns:: |l|l|p{4in}|
113
114=============  ===============  ====================================================
115  key            sub-key        explanation
116=============  ===============  ====================================================
117newCellDict    \                dict with lattice parameters computed by
118                                :func:`GSASIIstrMath.GetNewCellParms` (dict)
119title          \                Name of gpx file(?) (str)
120variables      \                Values for all N refined variables
121                                (list of float values, length N,
122                                ordered to match varyList)
123sig            \                Uncertainty values for all N refined variables
124                                (list of float values, length N,
125                                ordered to match varyList)
126varyList       \                List of directly refined variables
127                                (list of str values, length N)
128newAtomDict    \                dict with atom position values computed in
129                                :func:`GSASIIstrMath.ApplyXYZshifts` (dict)
130Rvals          \                R-factors, GOF, Marquardt value for last
131                                refinement cycle (dict)
132\              Nobs             Number of observed data points (int)
133\              Rwp              overall weighted profile R-factor (%, float)
134\              chisq            sum[w*(Iobs-Icalc)**2] for all data
135                                note this is not the reduced chi squared (float)
136\              lamMax           Marquardt value applied to Hessian diagonal
137                                (float)
138\              GOF              The goodness-of-fit, aka square root of
139                                the reduced chi squared. (float)
140covMatrix      \                The (NxN) covVariance matrix (np.array)
141=============  ===============  ====================================================
142
143Phase Tree Items
144----------------
145
146.. _Phase_table:
147
148.. index::
149   single: Phase object description
150   single: Data object descriptions; Phase
151
152Phase information is stored in the GSAS-II data tree as children of the
153Phases item in a dict with keys:
154
155.. tabularcolumns:: |l|l|p{4in}|
156
157==========  ===============  ====================================================
158  key         sub-key        explanation
159==========  ===============  ====================================================
160General         \            Overall information for the phase (dict)
161  \         AtomPtrs         list of four locations to use to pull info
162                             from the atom records (list)
163  \         F000X            x-ray F(000) intensity (float)
164  \         F000N            neutron F(000) intensity (float)
165  \         Mydir            directory of current .gpx file (str)
166  \         MCSA controls    Monte Carlo-Simulated Annealing controls (dict)
167  \         Cell             List with 8 items: cell refinement flag (bool)
168                             a, b, c, (Angstrom, float)
169                             alpha, beta & gamma (degrees, float)
170                             volume (A^3, float)
171  \         Type             'nuclear' or 'macromolecular' for now (str)
172  \         Map              dict of map parameters
173  \         SH Texture       dict of spherical harmonic preferred orientation
174                             parameters
175  \         Isotope          dict of isotopes for each atom type
176  \         Isotopes         dict of scattering lengths for each isotope
177                             combination for each element in phase 
178  \         Name             phase name (str)
179  \         SGData           Space group details as a :ref:`space group (SGData) object <SGData_table>`
180                             as defined in :func:`GSASIIspc.SpcGroup`.
181  \         Pawley neg wt    Restraint value for negative Pawley intensities
182                             (float)
183  \         Flip             dict of Charge flip controls
184  \         Data plot type   data plot type ('Mustrain', 'Size' or
185                             'Preferred orientation') for powder data (str)
186  \         Mass             Mass of unit cell contents in g/mol
187  \         POhkl            March-Dollase preferred orientation direction
188  \         Z                dict of atomic numbers for each atom type
189  \         vdWRadii         dict of van der Waals radii for each atom type
190  \         Color            Colors for atoms (list of (r,b,g) triplets)
191  \         AtomTypes        List of atom types
192  \         AtomMass         List of masses for atoms
193  \         doPawley         Flag for Pawley intensity extraction (bool)
194  \         NoAtoms          Number of atoms per unit cell of each type (dict)
195  \         Pawley dmin      maximum Q (as d-space) to use for Pawley
196                             extraction (float)
197  \         BondRadii        Default radius for each atom used to compute
198                             interatomic distances (list of floats)
199  \         AngleRadii       Default radius for each atom used to compute
200                             interatomic angles (list of floats)
201  \         DisAglCtls       Dict with distance/angle search controls,
202                             which has keys 'Name', 'AtomTypes',
203                             'BondRadii', 'AngleRadii' which are as above
204                             except are possibly edited. Also contains
205                             'Factors', which is a 2 element list with
206                             a multiplier for bond and angle search range
207                             [typically (0.85,0.85)].
208ranId           \            unique random number Id for phase (int)
209pId             \            Phase Id number for current project (int).
210Atoms           \            Atoms in phase as a list of lists. The outer list
211                             is for each atom, the inner list contains varying
212                             items depending on the type of phase, see
213                             the :ref:`Atom Records <Atoms_table>` description.
214                             (list of lists)
215Drawing         \            Display parameters (dict)
216\           ballScale        Size of spheres in ball-and-stick display (float)
217\           bondList         dict with bonds
218\           contourLevel     map contour level in e/A^3 (float)
219\           showABC          Flag to show view point triplet (bool). True=show.
220\           viewDir          cartesian viewing direction (np.array with three
221                             elements)
222\           Zclip            clipping distance in A (float)
223\           backColor        background for plot as and R,G,B triplet
224                             (default = [0, 0, 0], black).
225                             (list with three atoms)
226\           selectedAtoms    List of selected atoms (list of int values)
227\           showRigidBodies  Flag to highlight rigid body placement
228\           sizeH            Size ratio for H atoms (float)
229\           bondRadius       Size of binds in A (float)
230\           atomPtrs         positions of x, type, site sym, ADP flag in Draw Atoms (list)
231\           viewPoint        list of lists. First item in list is [x,y,z]
232                             in fractional coordinates for the center of
233                             the plot. Second item list of previous & current
234                             atom number viewed (may be [0,0])
235\           showHydrogen     Flag to control plotting of H atoms.
236\           unitCellBox      Flag to control display of the unit cell.
237\           ellipseProb      Probability limit for display of thermal
238                             ellipsoids in % (float).
239\           vdwScale         Multiplier of van der Waals radius for
240                             display of vdW spheres.
241\           Atoms            A list of lists with an entry for each atom
242                             that is plotted.
243\           Zstep            Step to de/increase Z-clip (float)
244\           Quaternion       Viewing quaternion (4 element np.array)
245\           radiusFactor     Distance ratio for searching for bonds. ? Bonds
246                             are located that are within r(Ra+Rb) and (Ra+Rb)/r
247                             where Ra and Rb are the atomic radii.
248\           oldxy            previous view point (list with two floats)
249\           cameraPos        Viewing position in A for plot (float)
250\           depthFog         True if use depthFog on plot - set currently as False (bool)
251RBModels        \            Rigid body assignments (note Rigid body definitions
252                             are stored in their own main top-level tree entry.)
253Pawley ref      \            Pawley reflections
254Histograms      \            A dict of dicts. The key for the outer dict is
255                             the histograms tied to this phase. The inner
256                             dict contains the combined phase/histogram
257                             parameters for items such as scale factors,
258                             size and strain parameters. (dict)
259MCSA            \            Monte-Carlo simulated annealing parameters (dict)
260\           
261==========  ===============  ====================================================
262
263Rigid Body Objects
264------------------
265
266.. _RBData_table:
267
268.. index::
269   single: Rigid Body Data description
270   single: Data object descriptions; Rigid Body Data
271   
272Rigid body descriptions are available for two types of rigid bodies: 'Vector'
273and 'Residue'. Vector rigid bodies are developed by a sequence of translations each
274with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates
275with defined refinable torsion angles.
276
277.. tabularcolumns:: |l|l|p{4in}|
278
279==========  ===============  ====================================================
280  key         sub-key        explanation
281==========  ===============  ====================================================
282Vector      RBId             vector rigid bodies (dict of dict)
283\           AtInfo           Drad, Color: atom drawing radius & color for each atom type (dict)
284\           RBname           Name assigned by user to rigid body (str)
285\           VectMag          vector magnitudes in A (list)
286\           rbXYZ            Cartesian coordinates for Vector rigid body (list of 3 float)
287\           rbRef            3 assigned reference atom nos. in rigid body for origin
288                             definition, use center of atoms flag (list of 3 int & 1 bool)
289\           VectRef          refinement flags for VectMag values (list of bool)
290\           rbTypes          Atom types for each atom in rigid body (list of str)
291\           rbVect           Cartesian vectors for each translation used to build rigid body (list of lists)
292\           useCount         Number of times rigid body is used in any structure (int)
293Residue     RBId             residue rigid bodies (dict of dict)
294\           AtInfo           Drad, Color: atom drawing radius & color for each atom type(dict)
295\           RBname           Name assigned by user to rigid body (str)
296\           rbXYZ            Cartesian coordinates for Residue rigid body (list of 3 float)
297\           rbTypes          Atom types for each atom in rigid body (list of str)
298\           atNames          Names of each atom in rigid body (e.g. C1,N2...) (list of str)
299\           rbRef            3 assigned reference atom nos. in rigid body for origin
300                             definition, use center of atoms flag (list of 3 int & 1 bool)
301\           rbSeq            Orig,Piv,angle,Riding (list): definition of internal rigid body
302                             torsion; origin atom (int), pivot atom (int), torsion angle (float),
303                             riding atoms (list of int)
304\           SelSeq           [int,int] used by SeqSizer to identify objects
305\           useCount         Number of times rigid body is used in any structure (int)
306RBIds           \            unique Ids generated upon creation of each rigid body (dict)
307\           Vector           Ids for each Vector rigid body (list)
308\           Residue          Ids for each Residue rigid body (list)
309==========  ===============  ====================================================
310
311Space Group Objects
312-------------------
313
314.. _SGData_table:
315
316.. index::
317   single: Space Group Data description
318   single: Data object descriptions; Space Group Data
319
320Space groups are interpreted by :func:`GSASIIspc.SpcGroup`
321and the information is placed in a SGdata object
322which is a dict with these keys:
323
324.. tabularcolumns:: |l|p{4.5in}|
325
326==========  ====================================================
327  key         explanation
328==========  ====================================================
329SpGrp       space group symbol (str)
330Laue        one of the following 14 Laue classes:
331            -1, 2/m, mmm, 4/m, 4/mmm, 3R,
332            3mR, 3, 3m1, 31m, 6/m, 6/mmm, m3, m3m (str)
333SGInv       True if centrosymmetric, False if not (bool)
334SGLatt      Lattice centering type. Will be one of
335            P, A, B, C, I, F, R (str)
336SGUniq      unique axis if monoclinic. Will be
337            a, b, or c for monoclinic space groups.
338            Will be blank for non-monoclinic. (str)
339SGCen       Symmetry cell centering vectors. A (n,3) np.array
340            of centers. Will always have at least one row:
341            ``np.array([[0, 0, 0]])``
342SGOps       symmetry operations as a list of form
343            ``[[M1,T1], [M2,T2],...]``
344            where :math:`M_n` is a 3x3 np.array
345            and :math:`T_n` is a length 3 np.array.
346            Atom coordinates are transformed where the
347            Asymmetric unit coordinates [X is (x,y,z)]
348            are transformed using
349            :math:`X^\prime = M_n*X+T_n`
350SGSys       symmetry unit cell: type one of
351            'triclinic', 'monoclinic', 'orthorhombic',
352            'tetragonal', 'rhombohedral', 'trigonal',
353            'hexagonal', 'cubic' (str)
354SGPolax     Axes for space group polarity. Will be one of
355            '', 'x', 'y', 'x y', 'z', 'x z', 'y z',
356            'xyz'. In the case where axes are arbitrary
357            '111' is used (P 1, and ?).
358==========  ====================================================
359
360Atom Records
361------------
362
363.. _Atoms_table:
364
365.. index::
366   single: Atoms record description
367   single: Data object descriptions; Atoms record
368
369
370If ``phasedict`` points to the phase information in the data tree, then
371atoms are contained in a list of atom records (list) in
372``phasedict['Atoms']``. Also needed to read atom information
373are four pointers, ``cx,ct,cs,cia = phasedict['General']['atomPtrs']``,
374which define locations in the atom record, as shown below. Items shown are
375always present; additional ones for macromolecular phases are marked 'mm'
376
377.. tabularcolumns:: |l|p{4.5in}|
378
379==============   ====================================================
380location         explanation
381==============   ====================================================
382ct-4              mm - residue number (str)
383ct-3              mm - residue name (e.g. ALA) (str)
384ct-2              mm - chain label (str)
385ct-1              atom label (str)
386ct                atom type (str)
387ct+1              refinement flags; combination of 'F', 'X', 'U' (str)
388cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
389cs                site symmetry (str)
390cs+1              site multiplicity (int)
391cia               ADP flag: Isotropic ('I') or Anisotropic ('A')
392cia+1             Uiso (float)
393cia+2...cia+7     U11, U22, U33, U12, U13, U23 (6 floats)
394atom[cia+8]       unique atom identifier (int)
395
396==============   ====================================================
397
398Drawing Atom Records
399--------------------
400
401.. _Drawing_atoms_table:
402
403.. index::
404   single: Drawing atoms record description
405   single: Data object descriptions; Drawing atoms record
406
407
408If ``phasedict`` points to the phase information in the data tree, then
409drawing atoms are contained in a list of drawing atom records (list) in
410``phasedict['Drawing']['Atoms']``. Also needed to read atom information
411are four pointers, ``cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs']``,
412which define locations in the atom record, as shown below. Items shown are
413always present; additional ones for macromolecular phases are marked 'mm'
414
415.. tabularcolumns:: |l|p{4.5in}|
416
417==============   ====================================================
418location         explanation
419==============   ====================================================
420ct-4              mm - residue number (str)
421ct-3              mm - residue name (e.g. ALA) (str)
422ct-2              mm - chain label (str)
423ct-1              atom label (str)
424ct                atom type (str)
425cx,cx+1,cx+2      the x,y and z coordinates (3 floats)
426cs-1              Sym Op symbol; sym. op number + unit cell id (e.g. '1,0,-1') (str)
427cs                atom drawing style; e.g. 'balls & sticks' (str)
428cs+1              atom label style (e.g. 'name') (str)
429cs+2              atom color (RBG triplet) (int)
430cs+3              ADP flag: Isotropic ('I') or Anisotropic ('A')
431cs+4              Uiso (float)
432cs+5...cs+11      U11, U22, U33, U12, U13, U23 (6 floats)
433ci                unique atom identifier; matches source atom Id in Atom Records (int)
434==============   ====================================================
435
436Powder Diffraction Tree Items
437-----------------------------
438
439.. _Powder_table:
440
441.. index::
442   single: Powder data object description
443   single: Data object descriptions; Powder Data
444
445Every powder diffraction histogram is stored in the GSAS-II data tree
446with a top-level entry named beginning with the string "PWDR ". The
447diffraction data for that information are directly associated with
448that tree item and there are a series of children to that item. The
449routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
450and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
451load this information into a dictionary where the child tree name is
452used as a key, and the information in the main entry is assigned
453a key of ``Data``, as outlined below.
454
455.. tabularcolumns:: |l|l|p{4in}|
456
457======================  ===============  ====================================================
458  key                      sub-key        explanation
459======================  ===============  ====================================================
460Comments                      \           Text strings extracted from the original powder
461                                          data header. These cannot be changed by the user;
462                                          it may be empty.
463Limits                       \            A list of two two element lists, as [[Ld,Hd],[L,H]]
464                                          where L and Ld are the current and default lowest
465                                          two-theta value to be used and
466                                          where H and Hd are the current and default highest
467                                          two-theta value to be used.
468Reflection Lists              \           A dict with an entry for each phase in the
469                                          histogram. The contents of each dict item
470                                          is a dict containing reflections, as described in
471                                          the :ref:`Powder Reflections <PowderRefl_table>`
472                                          description.
473Instrument Parameters         \           A list containing two dicts where the possible
474                                          keys in each dict are listed below. The value
475                                          for each item is a list containing three values:
476                                          the initial value, the current value and a
477                                          refinement flag which can have a value of
478                                          True, False or 0 where 0 indicates a value that
479                                          cannot be refined. The first and second
480                                          values are floats unless otherwise noted.
481                                          Items in the first dict are noted as [1]
482\                         Lam             Specifies a wavelength in Angstroms [1]
483\                         Lam1            Specifies the primary wavelength in
484                                          Angstrom, when an alpha1, alpha2
485                                          source is used [1]
486\                         Lam2            Specifies the secondary wavelength in
487                                          Angstrom, when an alpha1, alpha2
488                                          source is used [1]
489                          I(L2)/I(L1)     Ratio of Lam2 to Lam1 [1]           
490\                         Type            Histogram type (str) [1]:
491                                           * 'PXC' for constant wavelength x-ray
492                                           * 'PNC' for constant wavelength neutron
493                                           * 'PNT' for time of flight neutron
494\                         Zero            Two-theta zero correction in *degrees* [1]
495\                         Azimuth         Azimuthal setting angle for data recorded
496                                          with differing setting angles [1]
497\                         U, V, W         Cagliotti profile coefficients
498                                          for Gaussian instrumental broadening, where the
499                                          FWHM goes as
500                                          :math:`U \\tan^2\\theta + V \\tan\\theta + W` [1]
501\                         X, Y            Cauchy (Lorentzian) instrumental broadening
502                                          coefficients [1]
503\                         SH/L            Variant of the Finger-Cox-Jephcoat asymmetric
504                                          peak broadening ratio. Note that this is the
505                                          average between S/L and H/L where S is
506                                          sample height, H is the slit height and
507                                          L is the goniometer diameter. [1]
508\                         Polariz.        Polarization coefficient. [1]
509wtFactor                      \           A weighting factor to increase or decrease
510                                          the leverage of data in the histogram (float).
511                                          A value of 1.0 weights the data with their
512                                          standard uncertainties and a larger value
513                                          increases the weighting of the data (equivalent
514                                          to decreasing the uncertainties).
515Sample Parameters             \           Specifies a dict with parameters that describe how
516                                          the data were collected, as listed
517                                          below. Refinable parameters are a list containing
518                                          a float and a bool, where the second value
519                                          specifies if the value is refined, otherwise
520                                          the value is a float unless otherwise noted.
521\                         Scale           The histogram scale factor (refinable)
522\                         Absorption      The sample absorption coefficient as
523                                          :math:`\\mu r` where r is the radius
524                                          (refinable). Only valid for Debye-Scherrer geometry.
525\                         SurfaceRoughA   Surface roughness parameter A as defined by
526                                          Surotti,J. Appl. Cryst, 5,325-331, 1972.(refinable -
527                                          only valid for Bragg-Brentano geometry)                                         
528\                         SurfaceRoughB   Surface roughness parameter B (refinable -
529                                          only valid for Bragg-Brentano geometry)                                         
530\                         DisplaceX,      Sample displacement from goniometer center
531                          DisplaceY       where Y is along the beam direction and
532                                          X is perpendicular. Units are :math:`\\mu m`
533                                          (refinable).
534\                         Phi, Chi,       Goniometer sample setting angles, in degrees.
535                          Omega
536\                         Gonio. radius   Radius of the diffractometer in mm
537\                         InstrName       A name for the instrument, used in preparing
538                                          a CIF (str).
539\                         Force,          Variables that describe how the measurement
540                          Temperature,    was performed. Not used directly in
541                          Humidity,       any computations.
542                          Pressure,
543                          Voltage
544\                         ranId           The random-number Id for the histogram
545                                          (same value as where top-level key is ranId)
546\                         Type            Type of diffraction data, may be 'Debye-Scherrer'
547                                          or 'Bragg-Brentano' (str).
548\                         Diffuse         not in use?
549hId                           \           The number assigned to the histogram when
550                                          the project is loaded or edited (can change)
551ranId                         \           A random number id for the histogram
552                                          that does not change
553Background                    \           The background is stored as a list with where
554                                          the first item in the list is list and the second
555                                          item is a dict. The list contains the background
556                                          function and its coefficients; the dict contains
557                                          Debye diffuse terms and background peaks.
558                                          (TODO: this needs to be expanded.)
559Data                          \           The data consist of a list of 6 np.arrays
560                                          containing in order:
561
562                                           0. the x-postions (two-theta in degrees),
563                                           1. the intensity values (Yobs),
564                                           2. the weights for each Yobs value
565                                           3. the computed intensity values (Ycalc)
566                                           4. the background values
567                                           5. Yobs-Ycalc
568======================  ===============  ====================================================
569
570Powder Reflection Data Structure
571--------------------------------
572
573.. _PowderRefl_table:
574
575.. index::
576   single: Powder reflection object description
577   single: Data object descriptions; Powder Reflections
578   
579For every phase in a histogram, the ``Reflection Lists`` value is a dict
580one element of which is `'RefList'`, which is a np.array containing
581reflections. The columns in that array are documented below.
582
583==========  ====================================================
584  index         explanation
585==========  ====================================================
586 0,1,2       h,k,l (float)
587 3           multiplicity
588 4           d-space, Angstrom
589 5           pos, two-theta
590 6           sig, Gaussian width
591 7           gam, Lorenzian width
592 8           :math:`F_{obs}^2`
593 9           :math:`F_{calc}^2`
594 10          reflection phase, in degrees
595 11          intensity correction for reflection, this times
596             :math:`F_{obs}^2` or :math:`F_{calc}^2` gives Iobs or Icalc
597==========  ====================================================
598
599Single Crystal Tree Items
600-------------------------
601
602.. _Xtal_table:
603
604.. index::
605   single: Single Crystal data object description
606   single: Data object descriptions; Single crystal data
607
608Every single crystal diffraction histogram is stored in the GSAS-II data tree
609with a top-level entry named beginning with the string "HKLF ". The
610diffraction data for that information are directly associated with
611that tree item and there are a series of children to that item. The
612routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
613and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
614load this information into a dictionary where the child tree name is
615used as a key, and the information in the main entry is assigned
616a key of ``Data``, as outlined below.
617
618.. tabularcolumns:: |l|l|p{4in}|
619
620======================  ===============  ====================================================
621  key                      sub-key        explanation
622======================  ===============  ====================================================
623Data                          \           A dict that contains the
624                                          reflection table,
625                                          as described in the
626                                          :ref:`Single Crystal Reflections
627                                          <XtalRefl_table>`
628                                          description.
629
630Instrument Parameters         \           A list containing two dicts where the possible
631                                          keys in each dict are listed below. The value
632                                          for most items is a list containing two values:
633                                          the initial value, the current value.
634                                          The first and second
635                                          values are floats unless otherwise noted.
636\                         Lam             Specifies a wavelength in Angstroms (two floats)
637\                         Type            Histogram type (two str values):
638                                           * 'SXC' for constant wavelength x-ray
639                                           * 'SNC' for constant wavelength neutron
640                                           * 'SNT' for time of flight neutron
641\                         InstrName       A name for the instrument, used in preparing
642                                          a CIF (str).
643
644wtFactor                      \           A weighting factor to increase or decrease
645                                          the leverage of data in the histogram (float).
646                                          A value of 1.0 weights the data with their
647                                          standard uncertainties and a larger value
648                                          increases the weighting of the data (equivalent
649                                          to decreasing the uncertainties).
650
651hId                           \           The number assigned to the histogram when
652                                          the project is loaded or edited (can change)
653ranId                         \           A random number id for the histogram
654                                          that does not change
655======================  ===============  ====================================================
656
657Single Crystal Reflection Data Structure
658----------------------------------------
659
660.. _XtalRefl_table:
661
662.. index::
663   single: Single Crystal reflection object description
664   single: Data object descriptions; Single Crystal Reflections
665   
666For every single crystal a histogram, the ``'Data'`` item contains
667the structure factors as an np.array in item `'RefList'`.
668The columns in that array are documented below.
669
670==========  ====================================================
671  index         explanation
672==========  ====================================================
673 0,1,2       h,k,l (float)
674 3           multiplicity
675 4           d-space, Angstrom
676 5           :math:`F_{obs}^2`
677 6           :math:`\sigma(F_{obs}^2)`
678 7           :math:`F_{calc}^2`
679 8           :math:`F_{obs}^2T`
680 9           :math:`F_{calc}^2T`
681 10          reflection phase, in degrees
682 11          intensity correction for reflection, this times
683             :math:`F_{obs}^2` or :math:`F_{calc}^2`
684             gives Iobs or Icalc
685==========  ====================================================
686
687Image Data Structure
688--------------------
689
690.. _Image_table:
691
692.. index::
693   image: Image data object description
694   image: Image object descriptions
695   
696Every 2-dimensional image is stored in the GSAS-II data tree
697with a top-level entry named beginning with the string "IMG ". The
698image data are directly associated with that tree item and there
699are a series of children to that item. The routines :func:`GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
700and :func:`GSASIIstrIO.GetUsedHistogramsAndPhases` will
701load this information into a dictionary where the child tree name is
702used as a key, and the information in the main entry is assigned
703a key of ``Data``, as outlined below.
704
705.. tabularcolumns:: |l|l|p{4in}|
706
707======================  ======================  ====================================================
708  key                      sub-key              explanation
709======================  ======================  ====================================================
710Comments                       \                Text strings extracted from the original image data
711                                                header or a metafile. These cannot be changed by 
712                                                the user; it may be empty.                                               
713Image Controls              azmthOff            (float) The offset to be applied to an azimuthal
714                                                value. Accomodates
715                                                detector orientations other than with the detector
716                                                X-axis
717                                                horizontal.
718\                           background image    (list:str,float) The name of a tree item ("IMG ...") that is to be subtracted
719                                                during image integration multiplied by value. It must have the same size/shape as
720                                                the integrated image. NB: value < 0 for subtraction.
721\                           calibrant           (str) The material used for determining the position/orientation
722                                                of the image. The data is obtained from :func:`ImageCalibrants`
723                                                and UserCalibrants.py (supplied by user).
724\                           calibdmin           (float) The minimum d-spacing used during the last calibration run.
725\                           calibskip           (int) The number of expected diffraction lines skipped during the last
726                                                calibration run.
727\                           center              (list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam
728                                                strikes the detector plane as determined by calibration. This point
729                                                does not have to be within the limits of the detector boundaries.
730\                           centerAzm           (bool) If True then the azimuth reported for the integrated slice
731                                                of the image is at the center line otherwise it is at the leading edge.
732\                           color               (str) The name of the colormap used to display the image. Default = 'Paired'.
733\                           cutoff              (float) The minimum value of I/Ib for a point selected in a diffraction ring for
734                                                calibration calculations. See pixLimit for details as how point is found.           
735\                           DetDepth            (float) Coefficient for penetration correction to distance; accounts for diffraction
736                                                ring offset at higher angles. Optionally determined by calibration.
737\                           DetDepthRef         (bool) If True then refine DetDepth during calibration/recalibration calculation.
738\                           distance            (float) The distance (mm) from sample to detector plane.
739\                           ellipses            (list:lists) Each object in ellipses is a list [center,phi,radii,color] where
740                                                center (list) is location (mm) of the ellipse center on the detector plane, phi is the
741                                                rotation of the ellipse minor axis from the x-axis, and radii are the minor & major
742                                                radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color
743                                                is the selected drawing color (one of 'b', 'g' ,'r') for the ellipse/hyperbola.
744\                           edgemin             (float) Not used;  parameter in EdgeFinder code.
745\                           fullIntegrate       (bool) If True then integrate over full 360 deg azimuthal range.
746\                           GonioAngles         (list:floats) The 'Omega','Chi','Phi' goniometer angles used for this image.
747                                                Required for texture calculations.
748\                           invert_x            (bool) If True display the image with the x-axis inverted.
749\                           invert_y            (bool) If True display the image with the y-axis inverted.
750\                           IOtth               (list:floats) The minimum and maximum 2-theta values to be used for integration.
751\                           LRazimuth           (list:floats) The minimum and maximum azimuth values to be used for integration.
752\                           Oblique             (list:float,bool) If True apply a detector absorption correction using the value to the
753                                                intensities obtained during integration.
754\                           outAzimuths         (int) The number of azimuth pie slices.
755\                           outChannels         (int) The number of 2-theta steps.
756\                           pixelSize           (list:ints) The X,Y dimensions (microns) of each pixel.
757\                           pixLimit            (int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum.
758                                                This value (I) along with the minimum (Ib) in the box is reported by :func:`GSASIIimage.ImageLocalMax`
759                                                and subject to cutoff in :func:`GSASIIimage.makeRing`.
760                                                Locations are used to construct rings of points for calibration calcualtions.
761\                           PolaVal             (list:float,bool) If type='SASD' and if True, apply polarization correction to intensities from
762                                                integration using value.
763\                           rings               (list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a
764                                                diffraction ring with the same d-spacing (dsp)
765\                           ring                (list) The x,y coordinates of the >5 points on an inner ring
766                                                selected by the user,
767\                           Range               (list) The minimum & maximum values of the image
768\                           rotation            (float) The angle between the x-axis and the vector about which the
769                                                detector is tilted. Constrained to -180 to 180 deg.     
770\                           SampleShape         (str) Currently only 'Cylinder'. Sample shape for Debye-Scherrer experiments; used for absorption
771                                                calculations.
772\                           SampleAbs           (list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True
773                                                to cause correction to be applied.
774\                           setDefault          (bool) If True the use the image controls values for all new images to be read. (might be removed)
775\                           setRings            (bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.           
776\                           showLines           (bool) If True then isplay the integration limits to be used.
777\                           size                (list:int) The number of pixels on the image x & y axes
778\                           type                (str) One of 'PWDR', 'SASD' or 'REFL' for powder, small angle or reflectometry data, respectively.
779\                           tilt                (float) The angle the detector normal makes with the incident beam; range -90 to 90.
780\                           wavelength          (float) Tha radiation wavelength (Angstroms) as entered by the user (or someday obtained from the image header).
781                                               
782Masks                       Arcs                (list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask
783                                                to be excluded from integration
784\                           Frames              (list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside
785                                                of which is excluded from recalibration and integration. Only one frame is allowed.
786\                           Points              (list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded
787                                                from integration.
788\                           Polygons            (list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image
789                                                to be excluded from integration.
790\                           Rings               (list: lists) Each entry [2-theta,thickness] describes a ring mask
791                                                to be excluded from integration.
792\                           Thresholds          (list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included
793                                                in integrsation. The tuple is the image intensity limits and the list are those set by the user.   
794                                               
795Stress/Strain               Sample phi          (float) Sample rotation about vertical axis.
796\                           Sample z            (float) Sample translation from the calibration sample position (for Sample phi = 0)
797                                                These will be restricted by space group symmetry; result of strain fit refinement.
798\                           Type                (str) 'True' or 'Conventional': The strain model used for the calculation.
799\                           d-zero              (list:dict) Each item is for a diffraction ring on the image; all items are from the same phase
800                                                and are used to determine the strain tensor.
801                                                The dictionary items are:
802                                                'Dset': (float) True d-spacing for the diffraction ring; entered by the user.
803                                                'Dcalc': (float) Average calculated d-spacing determined from strain coeff.
804                                                'Emat': (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0)
805                                                'Esig': (list: float) Esds for Emat from fitting.
806                                                'pixLimit': (int) Search range to find highest point on ring for each data point
807                                                'cutoff': (float) I/Ib cutoff for searching.
808                                                'ImxyObs': (list: lists) [[X],[Y]] observed points to be used for strain calculations.
809                                                'ImtaObs': (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs.
810                                                'ImtaCalc': (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.
811                                               
812======================  ======================  ====================================================
813
814Parameter Dictionary
815-------------------------
816
817.. _parmDict_table:
818
819.. index::
820   single: Parameter dictionary
821
822The parameter dictionary contains all of the variable parameters for the refinement.
823The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>).
824It is prepared in two ways. When loaded from the tree
825(in :meth:`GSASII.GSASII.MakeLSParmDict` and
826:meth:`GSASIIIO.ExportBaseclass.loadParmDict`),
827the values are lists with two elements: ``[value, refine flag]``
828
829When loaded from the GPX file (in
830:func:`GSASIIstrMain.Refine` and :func:`GSASIIstrMain.SeqRefine`), the value in the
831dict is the actual parameter value (usually a float, but sometimes a
832letter or string flag value (such as I or A for iso/anisotropic).
833
834
835*Classes and routines*
836----------------------
837
838'''
839import re
840import imp
841import random as ran
842import sys
843import GSASIIpath
844import GSASIImath as G2mth
845import numpy as np
846
847GSASIIpath.SetVersionNumber("$Revision: 1790 $")
848
849DefaultControls = {
850    'deriv type':'analytic Hessian',
851    'min dM/M':0.0001,'shift factor':1.,'max cyc':3,'F**2':False,
852    'UsrReject':{'minF/sig':0,'MinExt':0.01,'MaxDF/F':100.,'MaxD':500.,'MinD':0.05},
853    'Copy2Next':False,'Reverse Seq':False,
854    'Author':'no name',
855    'FreePrm1':'Sample humidity (%)',
856    'FreePrm2':'Sample voltage (V)',
857    'FreePrm3':'Applied load (MN)',
858    'SeqPseudoVars':{},'SeqParFitEqList':[],'ShowCell':False,
859    }
860'''Values to be used as defaults for the initial contents of the ``Controls``
861data tree item.
862'''
863
864def MakeUniqueLabel(lbl,labellist):
865    '''Make sure that every a label is unique against a list by adding
866    digits at the end until it is not found in list.
867
868    :param str lbl: the input label
869    :param list labellist: the labels that have already been encountered
870    :returns: lbl if not found in labellist or lbl with ``_1-9`` (or
871      ``_10-99``, etc.) appended at the end
872    '''
873    lbl = lbl.strip()
874    if not lbl: # deal with a blank label
875        lbl = '_1'
876    if lbl not in labellist:
877        labellist.append(lbl)
878        return lbl
879    i = 1
880    prefix = lbl
881    if '_' in lbl:
882        prefix = lbl[:lbl.rfind('_')]
883        suffix = lbl[lbl.rfind('_')+1:]
884        try:
885            i = int(suffix)+1
886        except: # suffix could not be parsed
887            i = 1
888            prefix = lbl
889    while prefix+'_'+str(i) in labellist:
890        i += 1
891    else:
892        lbl = prefix+'_'+str(i)
893        labellist.append(lbl)
894    return lbl
895
896PhaseIdLookup = {}
897'''dict listing phase name and random Id keyed by sequential phase index as a str;
898best to access this using :func:`LookupPhaseName`
899'''
900PhaseRanIdLookup = {}
901'''dict listing phase sequential index keyed by phase random Id;
902best to access this using :func:`LookupPhaseId`
903'''
904HistIdLookup = {}
905'''dict listing histogram name and random Id, keyed by sequential histogram index as a str;
906best to access this using :func:`LookupHistName`
907'''
908HistRanIdLookup = {}
909'''dict listing histogram sequential index keyed by histogram random Id;
910best to access this using :func:`LookupHistId`
911'''
912AtomIdLookup = {}
913'''dict listing for each phase index as a str, the atom label and atom random Id,
914keyed by atom sequential index as a str;
915best to access this using :func:`LookupAtomLabel`
916'''
917AtomRanIdLookup = {}
918'''dict listing for each phase the atom sequential index keyed by atom random Id;
919best to access this using :func:`LookupAtomId`
920'''
921ShortPhaseNames = {}
922'''a dict containing a possibly shortened and when non-unique numbered
923version of the phase name. Keyed by the phase sequential index.
924'''
925ShortHistNames = {}
926'''a dict containing a possibly shortened and when non-unique numbered
927version of the histogram name. Keyed by the histogram sequential index.
928'''
929
930VarDesc = {}
931''' This dictionary lists descriptions for GSAS-II variables,
932as set in :func:`CompileVarDesc`. See that function for a description
933for how keys and values are written.
934'''
935
936reVarDesc = {}
937''' This dictionary lists descriptions for GSAS-II variables with
938the same values as :attr:`VarDesc` except that keys have been compiled as
939regular expressions. Initialized in :func:`CompileVarDesc`.
940'''
941
942def IndexAllIds(Histograms,Phases):
943    '''Scan through the used phases & histograms and create an index
944    to the random numbers of phases, histograms and atoms. While doing this,
945    confirm that assigned random numbers are unique -- just in case lightning
946    strikes twice in the same place.
947
948    Note: this code assumes that the atom random Id (ranId) is the last
949    element each atom record.
950
951    This is called in three places (only): :func:`GSASIIstrIO.GetUsedHistogramsAndPhases`
952    (which loads the histograms and phases from a GPX file),
953    :meth:`~GSASII.GSASII.GetUsedHistogramsAndPhasesfromTree`
954    (which loads the histograms and phases from the data tree.) and
955    :meth:`GSASIIconstrGUI.UpdateConstraints`
956    (which displays & edits the constraints in a GUI)
957
958    TODO: do we need a lookup for rigid body variables?
959    '''
960    # process phases and atoms
961    PhaseIdLookup.clear()
962    PhaseRanIdLookup.clear()   
963    AtomIdLookup.clear()
964    AtomRanIdLookup.clear()
965    ShortPhaseNames.clear()
966    for ph in Phases:
967        cx,ct,cs,cia = Phases[ph]['General']['AtomPtrs']
968        ranId = Phases[ph]['ranId'] 
969        while ranId in PhaseRanIdLookup:
970            # Found duplicate random Id! note and reassign
971            print ("\n\n*** Phase "+str(ph)+" has repeated ranId. Fixing.\n")
972            Phases[ph]['ranId'] = ranId = ran.randint(0,sys.maxint)
973        pId = str(Phases[ph]['pId'])
974        PhaseIdLookup[pId] = (ph,ranId)
975        PhaseRanIdLookup[ranId] = pId
976        shortname = ph[:10]
977        while shortname in ShortPhaseNames.values():
978            shortname = ph[:8] + ' ('+ pId + ')'
979        ShortPhaseNames[pId] = shortname
980        AtomIdLookup[pId] = {}
981        AtomRanIdLookup[pId] = {}
982        for iatm,at in enumerate(Phases[ph]['Atoms']):
983            ranId = at[cia+8]
984            while ranId in AtomRanIdLookup[pId]: # check for dups
985                print ("\n\n*** Phase "+str(ph)+" atom "+str(iatm)+" has repeated ranId. Fixing.\n")
986                at[cia+8] = ranId = ran.randint(0,sys.maxint)
987            AtomRanIdLookup[pId][ranId] = str(iatm)
988            if Phases[ph]['General']['Type'] == 'macromolecular':
989                label = '%s_%s_%s_%s'%(at[ct-1],at[ct-3],at[ct-4],at[ct-2])
990            else:
991                label = at[ct-1]
992            AtomIdLookup[pId][str(iatm)] = (label,ranId)
993    # process histograms
994    HistIdLookup.clear()
995    HistRanIdLookup.clear()
996    ShortHistNames.clear()
997    for hist in Histograms:
998        ranId = Histograms[hist]['ranId']
999        while ranId in HistRanIdLookup:
1000            # Found duplicate random Id! note and reassign
1001            print ("\n\n*** Histogram "+str(hist)+" has repeated ranId. Fixing.\n")
1002            Histograms[hist]['ranId'] = ranId = ran.randint(0,sys.maxint)
1003        hId = str(Histograms[hist]['hId'])
1004        HistIdLookup[hId] = (hist,ranId)
1005        HistRanIdLookup[ranId] = hId
1006        shortname = hist[:15]
1007        while shortname in ShortHistNames.values():
1008            shortname = hist[:11] + ' ('+ hId + ')'
1009        ShortHistNames[hId] = shortname
1010
1011def LookupAtomId(pId,ranId):
1012    '''Get the atom number from a phase and atom random Id
1013
1014    :param int/str pId: the sequential number of the phase
1015    :param int ranId: the random Id assigned to an atom
1016
1017    :returns: the index number of the atom (str)
1018    '''
1019    if not AtomRanIdLookup:
1020        raise Exception,'Error: LookupAtomId called before IndexAllIds was run'
1021    if pId is None or pId == '':
1022        raise KeyError,'Error: phase is invalid (None or blank)'
1023    pId = str(pId)
1024    if pId not in AtomRanIdLookup:
1025        raise KeyError,'Error: LookupAtomId does not have phase '+pId
1026    if ranId not in AtomRanIdLookup[pId]:
1027        raise KeyError,'Error: LookupAtomId, ranId '+str(ranId)+' not in AtomRanIdLookup['+pId+']'
1028    return AtomRanIdLookup[pId][ranId]
1029
1030def LookupAtomLabel(pId,index):
1031    '''Get the atom label from a phase and atom index number
1032
1033    :param int/str pId: the sequential number of the phase
1034    :param int index: the index of the atom in the list of atoms
1035
1036    :returns: the label for the atom (str) and the random Id of the atom (int)
1037    '''
1038    if not AtomIdLookup:
1039        raise Exception,'Error: LookupAtomLabel called before IndexAllIds was run'
1040    if pId is None or pId == '':
1041        raise KeyError,'Error: phase is invalid (None or blank)'
1042    pId = str(pId)
1043    if pId not in AtomIdLookup:
1044        raise KeyError,'Error: LookupAtomLabel does not have phase '+pId
1045    if index not in AtomIdLookup[pId]:
1046        raise KeyError,'Error: LookupAtomLabel, ranId '+str(index)+' not in AtomRanIdLookup['+pId+']'
1047    return AtomIdLookup[pId][index]
1048
1049def LookupPhaseId(ranId):
1050    '''Get the phase number and name from a phase random Id
1051
1052    :param int ranId: the random Id assigned to a phase
1053    :returns: the sequential Id (pId) number for the phase (str)
1054    '''
1055    if not PhaseRanIdLookup:
1056        raise Exception,'Error: LookupPhaseId called before IndexAllIds was run'
1057    if ranId not in PhaseRanIdLookup:
1058        raise KeyError,'Error: LookupPhaseId does not have ranId '+str(ranId)
1059    return PhaseRanIdLookup[ranId]
1060
1061def LookupPhaseName(pId):
1062    '''Get the phase number and name from a phase Id
1063
1064    :param int/str pId: the sequential assigned to a phase
1065    :returns:  (phase,ranId) where phase is the name of the phase (str)
1066      and ranId is the random # id for the phase (int)
1067    '''
1068    if not PhaseIdLookup:
1069        raise Exception,'Error: LookupPhaseName called before IndexAllIds was run'
1070    if pId is None or pId == '':
1071        raise KeyError,'Error: phase is invalid (None or blank)'
1072    pId = str(pId)
1073    if pId not in PhaseIdLookup:
1074        raise KeyError,'Error: LookupPhaseName does not have index '+pId
1075    return PhaseIdLookup[pId]
1076
1077def LookupHistId(ranId):
1078    '''Get the histogram number and name from a histogram random Id
1079
1080    :param int ranId: the random Id assigned to a histogram
1081    :returns: the sequential Id (hId) number for the histogram (str)
1082    '''
1083    if not HistRanIdLookup:
1084        raise Exception,'Error: LookupHistId called before IndexAllIds was run'
1085    if ranId not in HistRanIdLookup:
1086        raise KeyError,'Error: LookupHistId does not have ranId '+str(ranId)
1087    return HistRanIdLookup[ranId]
1088
1089def LookupHistName(hId):
1090    '''Get the histogram number and name from a histogram Id
1091
1092    :param int/str hId: the sequential assigned to a histogram
1093    :returns:  (hist,ranId) where hist is the name of the histogram (str)
1094      and ranId is the random # id for the histogram (int)
1095    '''
1096    if not HistIdLookup:
1097        raise Exception,'Error: LookupHistName called before IndexAllIds was run'
1098    if hId is None or hId == '':
1099        raise KeyError,'Error: histogram is invalid (None or blank)'
1100    hId = str(hId)
1101    if hId not in HistIdLookup:
1102        raise KeyError,'Error: LookupHistName does not have index '+hId
1103    return HistIdLookup[hId]
1104
1105def fmtVarDescr(varname):
1106    '''Return a string with a more complete description for a GSAS-II variable
1107
1108    :param str varname: A full G2 variable name with 2 or 3 or 4
1109       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1110       
1111    :returns: a string with the description
1112    '''
1113    s,l = VarDescr(varname)
1114    return s+": "+l
1115
1116def VarDescr(varname):
1117    '''Return two strings with a more complete description for a GSAS-II variable
1118
1119    :param str name: A full G2 variable name with 2 or 3 or 4
1120       colons (<p>:<h>:name[:<a>] or <p>::RBname:<r>:<t>])
1121       
1122    :returns: (loc,meaning) where loc describes what item the variable is mapped
1123      (phase, histogram, etc.) and meaning describes what the variable does.
1124    '''
1125   
1126    # special handling for parameter names without a colons
1127    # for now, assume self-defining
1128    if varname.find(':') == -1:
1129        return "Global",varname
1130       
1131    l = getVarDescr(varname)
1132    if not l:
1133        return ("invalid variable name ("+str(varname)+")!"),""
1134#        return "invalid variable name!",""
1135
1136    if not l[-1]:
1137        l[-1] = "(variable needs a definition! Set it in CompileVarDesc)"
1138
1139    if len(l) == 3:         #SASD variable name!
1140        s = 'component:'+l[1]
1141        return s,l[-1]
1142    s = ""
1143    if l[0] is not None and l[1] is not None: # HAP: keep short
1144        if l[2] == "Scale": # fix up ambigous name
1145            l[5] = "Phase fraction"
1146        if l[0] == '*':
1147            lbl = 'all'
1148        else:
1149            lbl = ShortPhaseNames.get(l[0],'? #'+str(l[0]))
1150        if l[1] == '*':
1151            hlbl = 'all'
1152        else:
1153            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1154        if hlbl[:4] == 'HKLF':
1155            hlbl = 'Xtl='+hlbl[5:]
1156        elif hlbl[:4] == 'PWDR':
1157            hlbl = 'Pwd='+hlbl[5:]
1158        else:
1159            hlbl = 'Hist='+hlbl
1160        s = "Ph="+str(lbl)+" * "+str(hlbl)
1161    else:
1162        if l[2] == "Scale": # fix up ambigous name: must be scale factor, since not HAP
1163            l[5] = "Scale factor"
1164        if l[2] == 'Back': # background parameters are "special", alas
1165            s = 'Hist='+ShortHistNames.get(l[1],'? #'+str(l[1]))
1166            l[-1] += ' #'+str(l[3])
1167        elif l[4] is not None: # rigid body parameter
1168            lbl = ShortPhaseNames.get(l[0],'phase?')
1169            s = "Res #"+str(l[3])+" body #"+str(l[4])+" in "+str(lbl)
1170        elif l[3] is not None: # atom parameter,
1171            lbl = ShortPhaseNames.get(l[0],'phase?')
1172            try:
1173                albl = LookupAtomLabel(l[0],l[3])[0]
1174            except KeyError:
1175                albl = 'Atom?'
1176            s = "Atom "+str(albl)+" in "+str(lbl)
1177        elif l[0] == '*':
1178            s = "All phases "
1179        elif l[0] is not None:
1180            lbl = ShortPhaseNames.get(l[0],'phase?')
1181            s = "Phase "+str(lbl)
1182        elif l[1] == '*':
1183            s = 'All hists'
1184        elif l[1] is not None:
1185            hlbl = ShortHistNames.get(l[1],'? #'+str(l[1]))
1186            if hlbl[:4] == 'HKLF':
1187                hlbl = 'Xtl='+hlbl[5:]
1188            elif hlbl[:4] == 'PWDR':
1189                hlbl = 'Pwd='+hlbl[5:]
1190            else:
1191                hlbl = 'Hist='+hlbl
1192            s = str(hlbl)
1193    if not s:
1194        s = 'Global'
1195    return s,l[-1]
1196
1197def getVarDescr(varname):
1198    '''Return a short description for a GSAS-II variable
1199
1200    :param str name: A full G2 variable name with 2 or 3 or 4
1201       colons (<p>:<h>:name[:<a1>][:<a2>])
1202     
1203    :returns: a six element list as [`p`,`h`,`name`,`a1`,`a2`,`description`],
1204      where `p`, `h`, `a1`, `a2` are str values or `None`, for the phase number,
1205      the histogram number and the atom number; `name` will always be
1206      a str; and `description` is str or `None`.
1207      If the variable name is incorrectly formed (for example, wrong
1208      number of colons), `None` is returned instead of a list.
1209    '''
1210    l = varname.split(':')
1211    if len(l) == 2:     #SASD parameter name
1212        return varname,l[0],getDescr(l[1])
1213    if len(l) == 3:
1214        l += [None,None]
1215    elif len(l) == 4:
1216        l += [None]
1217    elif len(l) != 5:
1218        return None
1219    for i in (0,1,3,4):
1220        if l[i] == "":
1221            l[i] = None
1222    l += [getDescr(l[2])]
1223    return l
1224   
1225def CompileVarDesc():
1226    '''Set the values in the variable description lookup table (:attr:`VarDesc`)
1227    into :attr:`reVarDesc`. This is called in :func:`getDescr` so the initialization
1228    is always done before use.
1229
1230    Note that keys may contain regular expressions, where '[xyz]'
1231    matches 'x' 'y' or 'z' (equivalently '[x-z]' describes this as range of values).
1232    '.*' matches any string. For example::
1233
1234    'AUiso':'Atomic isotropic displacement parameter',
1235
1236    will match variable ``'p::AUiso:a'``.
1237    If parentheses are used in the key, the contents of those parentheses can be
1238    used in the value, such as::
1239
1240    'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1241
1242    will match ``AU11``, ``AU23``,.. and `U11`, `U23` etc will be displayed
1243    in the value when used.
1244   
1245    '''
1246    if reVarDesc: return # already done
1247    for key,value in {
1248        # derived or other sequential vars
1249        '([abc])$' : 'Lattice parameter, \\1, from Ai and Djk', # N.B. '$' prevents match if any characters follow
1250        u'\u03B1' : u'Lattice parameter, \u03B1, from Ai and Djk',
1251        u'\u03B2' : u'Lattice parameter, \u03B2, from Ai and Djk',
1252        u'\u03B3' : u'Lattice parameter, \u03B3, from Ai and Djk',
1253        # ambiguous, alas:
1254        'Scale' : 'Phase or Histogram scale factor',
1255        # Phase vars (p::<var>)
1256        'A([0-5])' : 'Reciprocal metric tensor component \\1',
1257        'Vol' : 'Unit cell volume',
1258        # Atom vars (p::<var>:a)
1259        'dA([xyz])$' : 'change to atomic coordinate, \\1',
1260        'A([xyz])$' : '\\1 fractional atomic coordinate',
1261        'AUiso':'Atomic isotropic displacement parameter',
1262        'AU([123][123])':'Atomic anisotropic displacement parameter U\\1',
1263        'Afrac': 'Atomic occupancy parameter',
1264        # Hist & Phase (HAP) vars (p:h:<var>)
1265        'Back': 'Background term',
1266        'BkPkint;(.*)':'Background peak #\\1 intensity',
1267        'BkPkpos;(.*)':'Background peak #\\1 position',
1268        'BkPksig;(.*)':'Background peak #\\1 Gaussian width',
1269        'BkPkgam;(.*)':'Background peak #\\1 Cauchy width',
1270        'Bab([AU])': 'Babinet solvent scattering coef. \\1',
1271        'D([123][123])' : 'Anisotropic strain coef. \\1',
1272        'Extinction' : 'Extinction coef.',
1273        'MD' : 'March-Dollase coef.',
1274        'Mustrain;.*' : 'Microstrain coef.',
1275        'Size;.*' : 'Crystallite size value',
1276        'eA$' : 'Cubic mustrain value',
1277        'Ep$' : 'Primary extinction',
1278        'Es$' : 'Secondary type II extinction',
1279        'Eg$' : 'Secondary type I extinction',
1280        #Histogram vars (:h:<var>)
1281        'Absorption' : 'Absorption coef.',
1282        'Displace([XY])' : 'Debye-Scherrer sample displacement \\1',
1283        'Lam' : 'Wavelength',
1284        'Polariz\.' : 'Polarization correction',
1285        'SH/L' : 'FCJ peak asymmetry correction',
1286        '([UVW])$' : 'Gaussian instrument broadening \\1',
1287        '([XY])$' : 'Cauchy instrument broadening \\1',
1288        'Zero' : 'Debye-Scherrer zero correction',
1289        'nDebye' : 'Debye model background corr. terms',
1290        'nPeaks' : 'Fixed peak background corr. terms',
1291        'RBV.*' : 'Vector rigid body parameter',
1292        'RBR.*' : 'Residue rigid body parameter',
1293        'RBRO([aijk])' : 'Residue rigid body orientation parameter',
1294        'RBRP([xyz])' : 'Residue rigid body position parameter',
1295        'RBRTr;.*' : 'Residue rigid body torsion parameter',
1296        'RBR([TLS])([123AB][123AB])' : 'Residue rigid body group disp. param.',
1297        'constr([0-9]*)' : 'Parameter from constraint',
1298        # supersymmetry parameters  p::<var>:a:o 'Flen','Fcent'?
1299        'mV([0-2])$' : 'Modulation vector component \\1',
1300        'Fsin'  :   'Sin site fraction modulation',
1301        'Fcos'  :   'Cos site fraction modulation',
1302        'Fzero'  :   'Crenel function offset',
1303        'Fwid'   :   'Crenel function width',
1304        'Tzero'  :   'Sawtooth/ZigZag location',
1305        '([XYZ])slope': 'Sawtooth/ZigZag slope for \\1',
1306        '([XYZ])sin'  : 'Sin position wave for \\1',
1307        '([XYZ])cos'  : 'Cos position wave for \\1',
1308        'U([123][123])sin$' :  'Sin thermal wave for U\\1',
1309        'U([123][123])cos$' :  'Cos thermal wave for U\\1',
1310        'M([XYZ])sin$' :  'Sin mag. moment wave for \\1',
1311        'M([XYZ])cos$' :  'Cos mag. moment wave for \\1',
1312        # SASD vars (l:<var>;l = component)
1313        'Aspect ratio' : 'Particle aspect ratio',
1314        'Length' : 'Cylinder length',
1315        'Diameter' : 'Cylinder/disk diameter',
1316        'Thickness' : 'Disk thickness',
1317        'Dist' : 'Interparticle distance',
1318        'VolFr' : 'Dense scatterer volume fraction',
1319        'epis' : 'Sticky sphere epsilon',
1320        'Sticky' : 'Stickyness',
1321        'Depth' : 'Well depth',
1322        'Width' : 'Well width',
1323        'Volume' : 'Particle volume',
1324        'Radius' : 'Sphere/cylinder/disk radius',
1325        'Mean' : 'Particle mean radius',
1326        'StdDev' : 'Standard deviation in Mean',
1327        'G$': 'Guinier prefactor',
1328        'Rg$': 'Guinier radius of gyration',
1329        'B$': 'Porod prefactor',
1330        'P$': 'Porod power',
1331        'Cutoff': 'Porod cutoff',
1332        'PkInt': 'Bragg peak intensity',
1333        'PkPos': 'Bragg peak position',
1334        'PkSig': 'Bragg peak sigma',
1335        'PkGam': 'Bragg peak gamma',
1336        'e([12][12])' : 'strain tensor e\1',   # strain vars e11, e22, e12
1337        'Dcalc': 'Calc. d-spacing',
1338        'Back$': 'background parameter',
1339        'pos$': 'peak position',
1340        'int$': 'peak intensity',
1341        }.items():
1342        VarDesc[key] = value
1343        reVarDesc[re.compile(key)] = value
1344
1345def getDescr(name):
1346    '''Return a short description for a GSAS-II variable
1347
1348    :param str name: The descriptive part of the variable name without colons (:)
1349     
1350    :returns: a short description or None if not found
1351    '''
1352
1353    CompileVarDesc() # compile the regular expressions, if needed
1354    for key in reVarDesc:
1355        m = key.match(name)
1356        if m:
1357            reVarDesc[key]
1358            return m.expand(reVarDesc[key])
1359    return None
1360
1361def GenWildCard(varlist):
1362    '''Generate wildcard versions of G2 variables. These introduce '*'
1363    for a phase, histogram or atom number (but only for one of these
1364    fields) but only when there is more than one matching variable in the
1365    input variable list. So if the input is this::
1366   
1367      varlist = ['0::AUiso:0', '0::AUiso:1', '1::AUiso:0']
1368
1369    then the output will be this::
1370   
1371       wildList = ['*::AUiso:0', '0::AUiso:*']
1372
1373    :param list varlist: an input list of GSAS-II variable names
1374      (such as 0::AUiso:0)
1375
1376    :returns: wildList, the generated list of wild card variable names.
1377    '''
1378    wild = []
1379    for i in (0,1,3):
1380        currentL = varlist[:]
1381        while currentL:
1382            item1 = currentL.pop(0)
1383            i1splt = item1.split(':')
1384            if i >= len(i1splt): continue
1385            if i1splt[i]:
1386                nextL = []
1387                i1splt[i] = '[0-9]+'
1388                rexp = re.compile(':'.join(i1splt))
1389                matchlist = [item1]
1390                for nxtitem in currentL:
1391                    if rexp.match(nxtitem):
1392                        matchlist += [nxtitem]
1393                    else:
1394                        nextL.append(nxtitem)
1395                if len(matchlist) > 1:
1396                    i1splt[i] = '*'
1397                    wild.append(':'.join(i1splt))
1398                currentL = nextL
1399    return wild
1400
1401def LookupWildCard(varname,varlist):
1402    '''returns a list of variable names from list varname
1403    that match wildcard name in varname
1404   
1405    :param str varname: a G2 variable name containing a wildcard
1406      (such as \*::var)
1407    :param list varlist: the list of all variable names used in
1408      the current project
1409    :returns: a list of matching GSAS-II variables (may be empty) 
1410    '''
1411    rexp = re.compile(varname.replace('*','[0-9]+'))
1412    return sorted([var for var in varlist if rexp.match(var)])
1413
1414
1415def _lookup(dic,key):
1416    '''Lookup a key in a dictionary, where None returns an empty string
1417    but an unmatched key returns a question mark. Used in :class:`G2VarObj`
1418    '''
1419    if key is None:
1420        return ""
1421    elif key == "*":
1422        return "*"
1423    else:
1424        return dic.get(key,'?')
1425
1426class G2VarObj(object):
1427    '''Defines a GSAS-II variable either using the phase/atom/histogram
1428    unique Id numbers or using a character string that specifies
1429    variables by phase/atom/histogram number (which can change).
1430    Note that :func:`LoadID` should be used to (re)load the current Ids
1431    before creating or later using the G2VarObj object.
1432
1433    This can store rigid body variables, but does not translate the residue # and
1434    body # to/from random Ids
1435
1436    A :class:`G2VarObj` object can be created with a single parameter:
1437   
1438    :param str/tuple varname: a single value can be used to create a :class:`G2VarObj`
1439      object. If a string, it must be of form "p:h:var" or "p:h:var:a", where
1440
1441     * p is the phase number (which may be left blank or may be '*' to indicate all phases);
1442     * h is the histogram number (which may be left blank or may be '*' to indicate all histograms);
1443     * a is the atom number (which may be left blank in which case the third colon is omitted).
1444       The atom number can be specified as '*' if a phase number is specified (not as '*').
1445       For rigid body variables, specify a will be a string of form "residue:body#"
1446
1447      Alternately a single tuple of form (Phase,Histogram,VarName,AtomID) can be used, where
1448      Phase, Histogram, and AtomID are None or are ranId values (or one can be '*')
1449      and VarName is a string. Note that if Phase is '*' then the AtomID is an atom number.
1450      For a rigid body variables, AtomID is a string of form "residue:body#".
1451
1452    If four positional arguments are supplied, they are:
1453
1454    :param str/int phasenum: The number for the phase (or None or '*')
1455    :param str/int histnum: The number for the histogram (or None or '*')
1456    :param str varname: a single value can be used to create a :class:`G2VarObj`
1457    :param str/int atomnum: The number for the atom (or None or '*')
1458   
1459    '''
1460    IDdict = {}
1461    IDdict['phases'] = {}
1462    IDdict['hists'] = {}
1463    IDdict['atoms'] = {}
1464    def __init__(self,*args):
1465        self.phase = None
1466        self.histogram = None
1467        self.name = ''
1468        self.atom = None
1469        if len(args) == 1 and (type(args[0]) is list or type(args[0]) is tuple) and len(args[0]) == 4:
1470            # single arg with 4 values
1471            self.phase,self.histogram,self.name,self.atom = args[0]
1472        elif len(args) == 1 and ':' in args[0]:
1473            #parse a string
1474            lst = args[0].split(':')
1475            if lst[0] == '*':
1476                self.phase = '*'
1477                if len(lst) > 3:
1478                    self.atom = lst[3]
1479                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1480            elif lst[1] == '*':           
1481                self.histogram = '*'
1482                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1483            else:
1484                self.histogram = HistIdLookup.get(lst[1],[None,None])[1]
1485                self.phase = PhaseIdLookup.get(lst[0],[None,None])[1]
1486                if len(lst) == 4:
1487                    if lst[3] == '*':
1488                        self.atom = '*'
1489                    else:
1490                        self.atom = AtomIdLookup[lst[0]].get(lst[3],[None,None])[1]
1491                elif len(lst) == 5:
1492                    self.atom = lst[3]+":"+lst[4]
1493                elif len(lst) == 3:
1494                    pass
1495                else:
1496                    raise Exception,"Too many colons in var name "+str(args[0])
1497            self.name = lst[2]
1498        elif len(args) == 4:
1499            if args[0] == '*':
1500                self.phase = '*'
1501                self.atom = args[3]
1502            else:
1503                self.phase = PhaseIdLookup.get(str(args[0]),[None,None])[1]
1504                if args[3] == '*':
1505                    self.atom = '*'
1506                elif args[0] is not None:
1507                    self.atom = AtomIdLookup[args[0]].get(str(args[3]),[None,None])[1]
1508            if args[1] == '*':
1509                self.histogram = '*'
1510            else:
1511                self.histogram = HistIdLookup.get(str(args[1]),[None,None])[1]
1512            self.name = args[2]
1513        else:
1514            raise Exception,"Incorrectly called GSAS-II parameter name"
1515
1516        #print "DEBUG: created ",self.phase,self.histogram,self.name,self.atom
1517
1518    def __str__(self):
1519        return self.varname()
1520
1521    def varname(self):
1522        '''Formats the GSAS-II variable name as a "traditional" GSAS-II variable
1523        string (p:h:<var>:a) or (p:h:<var>)
1524
1525        :returns: the variable name as a str
1526        '''
1527        a = ""
1528        if self.phase == "*":
1529            ph = "*"
1530            if self.atom:
1531                a = ":" + str(self.atom)
1532        else:
1533            ph = _lookup(PhaseRanIdLookup,self.phase)
1534            if self.atom == '*':
1535                a = ':*'
1536            elif self.atom:
1537                if ":" in str(self.atom):
1538                    a = ":" + str(self.atom)
1539                elif ph in AtomRanIdLookup:
1540                    a = ":" + AtomRanIdLookup[ph].get(self.atom,'?')
1541                else:
1542                    a = ":?"
1543        if self.histogram == "*":
1544            hist = "*"
1545        else:
1546            hist = _lookup(HistRanIdLookup,self.histogram)
1547        s = (ph + ":" + hist + ":" + str(self.name)) + a
1548        return s
1549   
1550    def __repr__(self):
1551        '''Return the detailed contents of the object
1552        '''
1553        s = "<"
1554        if self.phase == '*':
1555            s += "Phases: all; "
1556            if self.atom is not None:
1557                if ":" in str(self.atom):
1558                    s += "Rigid body" + str(self.atom) + "; "
1559                else:
1560                    s += "Atom #" + str(self.atom) + "; "
1561        elif self.phase is not None:
1562            ph =  _lookup(PhaseRanIdLookup,self.phase)
1563            s += "Phase: rId=" + str(self.phase) + " (#"+ ph + "); "
1564            if self.atom == '*':
1565                s += "Atoms: all; "
1566            elif ":" in self(self.atom):
1567                s += "Rigid body" + str(self.atom) + "; "
1568            elif self.atom is not None:
1569                s += "Atom rId=" + str(self.atom)
1570                if ph in AtomRanIdLookup:
1571                    s += " (#" + AtomRanIdLookup[ph].get(self.atom,'?') + "); "
1572                else:
1573                    s += " (#? -- not found!); "
1574        if self.histogram == '*':
1575            s += "Histograms: all; "
1576        elif self.histogram is not None:
1577            hist = _lookup(HistRanIdLookup,self.histogram)
1578            s += "Histogram: rId=" + str(self.histogram) + " (#"+ hist + "); "
1579        s += 'Variable name="' + str(self.name) + '">'
1580        return s+" ("+self.varname()+")"
1581
1582    def __eq__(self, other):
1583        if type(other) is type(self):
1584            return (self.phase == other.phase and
1585                    self.histogram == other.histogram and
1586                    self.name == other.name and
1587                    self.atom == other.atom)
1588        return False
1589
1590    def _show(self):
1591        'For testing, shows the current lookup table'
1592        print 'phases', self.IDdict['phases']
1593        print 'hists', self.IDdict['hists']
1594        print 'atomDict', self.IDdict['atoms']
1595
1596#==========================================================================
1597# shortcut routines
1598exp = np.exp
1599sind = sin = s = lambda x: np.sin(x*np.pi/180.)
1600cosd = cos = c = lambda x: np.cos(x*np.pi/180.)
1601tand = tan = t = lambda x: np.tan(x*np.pi/180.)
1602sqrt = sq = lambda x: np.sqrt(x)
1603pi = lambda: np.pi
1604class ExpressionObj(object):
1605    '''Defines an object with a user-defined expression, to be used for
1606    secondary fits or restraints. Object is created null, but is changed
1607    using :meth:`LoadExpression`. This contains only the minimum
1608    information that needs to be stored to save and load the expression
1609    and how it is mapped to GSAS-II variables.
1610    '''
1611    def __init__(self):
1612        self.expression = ''
1613        'The expression as a text string'
1614        self.assgnVars = {}
1615        '''A dict where keys are label names in the expression mapping to a GSAS-II
1616        variable. The value a G2 variable name.
1617        Note that the G2 variable name may contain a wild-card and correspond to
1618        multiple values.
1619        '''
1620        self.freeVars = {}
1621        '''A dict where keys are label names in the expression mapping to a free
1622        parameter. The value is a list with:
1623
1624         * a name assigned to the parameter
1625         * a value for to the parameter and
1626         * a flag to determine if the variable is refined.
1627        ''' 
1628        self.depVar = None
1629
1630        self.lastError = ('','')
1631        '''Shows last encountered error in processing expression
1632        (list of 1-3 str values)'''
1633
1634    def LoadExpression(self,expr,exprVarLst,varSelect,varName,varValue,varRefflag):
1635        '''Load the expression and associated settings into the object. Raises
1636        an exception if the expression is not parsed, if not all functions
1637        are defined or if not all needed parameter labels in the expression
1638        are defined.
1639
1640        This will not test if the variable referenced in these definitions
1641        are actually in the parameter dictionary. This is checked when the
1642        computation for the expression is done in :meth:`SetupCalc`.
1643       
1644        :param str expr: the expression
1645        :param list exprVarLst: parameter labels found in the expression
1646        :param dict varSelect: this will be 0 for Free parameters
1647          and non-zero for expression labels linked to G2 variables.
1648        :param dict varName: Defines a name (str) associated with each free parameter
1649        :param dict varValue: Defines a value (float) associated with each free parameter
1650        :param dict varRefflag: Defines a refinement flag (bool)
1651          associated with each free parameter
1652        '''
1653        self.expression = expr
1654        self.compiledExpr = None
1655        self.freeVars = {}
1656        self.assgnVars = {}
1657        for v in exprVarLst:
1658            if varSelect[v] == 0:
1659                self.freeVars[v] = [
1660                    varName.get(v),
1661                    varValue.get(v),
1662                    varRefflag.get(v),
1663                    ]
1664            else:
1665                self.assgnVars[v] = varName[v]
1666        self.CheckVars()
1667
1668    def EditExpression(self,exprVarLst,varSelect,varName,varValue,varRefflag):
1669        '''Load the expression and associated settings from the object into
1670        arrays used for editing.
1671
1672        :param list exprVarLst: parameter labels found in the expression
1673        :param dict varSelect: this will be 0 for Free parameters
1674          and non-zero for expression labels linked to G2 variables.
1675        :param dict varName: Defines a name (str) associated with each free parameter
1676        :param dict varValue: Defines a value (float) associated with each free parameter
1677        :param dict varRefflag: Defines a refinement flag (bool)
1678          associated with each free parameter
1679
1680        :returns: the expression as a str
1681        '''
1682        for v in self.freeVars:
1683            varSelect[v] = 0
1684            varName[v] = self.freeVars[v][0]
1685            varValue[v] = self.freeVars[v][1]
1686            varRefflag[v] = self.freeVars[v][2]
1687        for v in self.assgnVars:
1688            varSelect[v] = 1
1689            varName[v] = self.assgnVars[v]
1690        return self.expression
1691
1692    def GetVaried(self):
1693        'Returns the names of the free parameters that will be refined'
1694        return ["::"+self.freeVars[v][0] for v in self.freeVars if self.freeVars[v][2]]
1695
1696    def GetVariedVarVal(self):
1697        'Returns the names and values of the free parameters that will be refined'
1698        return [("::"+self.freeVars[v][0],self.freeVars[v][1]) for v in self.freeVars if self.freeVars[v][2]]
1699
1700    def UpdateVariedVars(self,varyList,values):
1701        'Updates values for the free parameters (after a refinement); only updates refined vars'
1702        for v in self.freeVars:
1703            if not self.freeVars[v][2]: continue
1704            if "::"+self.freeVars[v][0] not in varyList: continue
1705            indx = varyList.index("::"+self.freeVars[v][0])
1706            self.freeVars[v][1] = values[indx]
1707
1708    def GetIndependentVars(self):
1709        'Returns the names of the required independent parameters used in expression'
1710        return [self.assgnVars[v] for v in self.assgnVars]
1711
1712    def CheckVars(self):
1713        '''Check that the expression can be parsed, all functions are
1714        defined and that input loaded into the object is internally
1715        consistent. If not an Exception is raised.
1716
1717        :returns: a dict with references to packages needed to
1718          find functions referenced in the expression.
1719        '''
1720        ret = self.ParseExpression(self.expression)
1721        if not ret:
1722            raise Exception("Expression parse error")
1723        exprLblList,fxnpkgdict = ret
1724        # check each var used in expression is defined
1725        defined = self.assgnVars.keys() + self.freeVars.keys()
1726        notfound = []
1727        for var in exprLblList:
1728            if var not in defined:
1729                notfound.append(var)
1730        if notfound:
1731            msg = 'Not all variables defined'
1732            msg1 = 'The following variables were not defined: '
1733            msg2 = ''
1734            for var in notfound:
1735                if msg: msg += ', '
1736                msg += var
1737            self.lastError = (msg1,'  '+msg2)
1738            raise Exception(msg)
1739        return fxnpkgdict
1740
1741    def ParseExpression(self,expr):
1742        '''Parse an expression and return a dict of called functions and
1743        the variables used in the expression. Returns None in case an error
1744        is encountered. If packages are referenced in functions, they are loaded
1745        and the functions are looked up into the modules global
1746        workspace.
1747       
1748        Note that no changes are made to the object other than
1749        saving an error message, so that this can be used for testing prior
1750        to the save.
1751
1752        :returns: a list of used variables
1753        '''
1754        self.lastError = ('','')
1755        import ast
1756        def FindFunction(f):
1757            '''Find the object corresponding to function f
1758            :param str f: a function name such as 'numpy.exp'
1759            :returns: (pkgdict,pkgobj) where pkgdict contains a dict
1760              that defines the package location(s) and where pkgobj
1761              defines the object associated with the function.
1762              If the function is not found, pkgobj is None.
1763            '''
1764            df = f.split('.')
1765            pkgdict = {}
1766            # no listed package, try in current namespace
1767            if len(df) == 1: 
1768                try:
1769                    fxnobj = eval(f)
1770                    return pkgdict,fxnobj
1771                except (AttributeError, NameError):
1772                    return None,None
1773            else:
1774                try:
1775                    fxnobj = eval(f)
1776                    pkgdict[df[0]] = eval(df[0])
1777                    return pkgdict,fxnobj
1778                except (AttributeError, NameError):
1779                    pass
1780            # includes a package, lets try to load the packages
1781            pkgname = ''
1782            path = sys.path
1783            for pkg in f.split('.')[:-1]: # if needed, descend down the tree
1784                if pkgname:
1785                    pkgname += '.' + pkg
1786                else:
1787                    pkgname = pkg
1788                fp = None
1789                try:
1790                    fp, fppath,desc = imp.find_module(pkg,path)
1791                    pkgobj = imp.load_module(pkg,fp,fppath,desc)
1792                    pkgdict[pkgname] = pkgobj
1793                    path = [fppath]
1794                except Exception as msg:
1795                    print('load of '+pkgname+' failed with error='+str(msg))
1796                    return {},None
1797                finally:
1798                    if fp: fp.close()
1799                try:
1800                    #print 'before',pkgdict.keys()
1801                    fxnobj = eval(f,globals(),pkgdict)
1802                    #print 'after 1',pkgdict.keys()
1803                    #fxnobj = eval(f,pkgdict)
1804                    #print 'after 2',pkgdict.keys()
1805                    return pkgdict,fxnobj
1806                except:
1807                    continue
1808            return None # not found
1809        def ASTtransverse(node,fxn=False):
1810            '''Transverse a AST-parsed expresson, compiling a list of variables
1811            referenced in the expression. This routine is used recursively.
1812
1813            :returns: varlist,fxnlist where
1814              varlist is a list of referenced variable names and
1815              fxnlist is a list of used functions
1816            '''
1817            varlist = []
1818            fxnlist = []
1819            if isinstance(node, list):
1820                for b in node:
1821                    v,f = ASTtransverse(b,fxn)
1822                    varlist += v
1823                    fxnlist += f
1824            elif isinstance(node, ast.AST):
1825                for a, b in ast.iter_fields(node):
1826                    if isinstance(b, ast.AST):
1827                        if a == 'func': 
1828                            fxnlist += ['.'.join(ASTtransverse(b,True)[0])]
1829                            continue
1830                        v,f = ASTtransverse(b,fxn)
1831                        varlist += v
1832                        fxnlist += f
1833                    elif isinstance(b, list):
1834                        v,f = ASTtransverse(b,fxn)
1835                        varlist += v
1836                        fxnlist += f
1837                    elif node.__class__.__name__ == "Name":
1838                        varlist += [b]
1839                    elif fxn and node.__class__.__name__ == "Attribute":
1840                        varlist += [b]
1841            return varlist,fxnlist
1842        try:
1843            exprast = ast.parse(expr)
1844        except SyntaxError as err:
1845            s = ''
1846            import traceback
1847            for i in traceback.format_exc().splitlines()[-3:-1]:
1848                if s: s += "\n"
1849                s += str(i)
1850            self.lastError = ("Error parsing expression:",s)
1851            return
1852        # find the variables & functions
1853        v,f = ASTtransverse(exprast)
1854        varlist = sorted(list(set(v)))
1855        fxnlist = list(set(f))
1856        pkgdict = {}
1857        # check the functions are defined
1858        for fxn in fxnlist:
1859            fxndict,fxnobj = FindFunction(fxn)
1860            if not fxnobj:
1861                self.lastError = ("Error: Invalid function",fxn,
1862                                  "is not defined")
1863                return
1864            if not hasattr(fxnobj,'__call__'):
1865                self.lastError = ("Error: Not a function.",fxn,
1866                                  "cannot be called as a function")
1867                return
1868            pkgdict.update(fxndict)
1869        return varlist,pkgdict
1870
1871    def GetDepVar(self):
1872        'return the dependent variable, or None'
1873        return self.depVar
1874
1875    def SetDepVar(self,var):
1876        'Set the dependent variable, if used'
1877        self.depVar = var
1878#==========================================================================
1879class ExpressionCalcObj(object):
1880    '''An object used to evaluate an expression from a :class:`ExpressionObj`
1881    object.
1882   
1883    :param ExpressionObj exprObj: a :class:`~ExpressionObj` expression object with
1884      an expression string and mappings for the parameter labels in that object.
1885    '''
1886    def __init__(self,exprObj):
1887        self.eObj = exprObj
1888        'The expression and mappings; a :class:`ExpressionObj` object'
1889        self.compiledExpr = None
1890        'The expression as compiled byte-code'
1891        self.exprDict = {}
1892        '''dict that defines values for labels used in expression and packages
1893        referenced by functions
1894        '''
1895        self.lblLookup = {}
1896        '''Lookup table that specifies the expression label name that is
1897        tied to a particular GSAS-II parameters in the parmDict.
1898        '''
1899        self.fxnpkgdict = {}
1900        '''a dict with references to packages needed to
1901        find functions referenced in the expression.
1902        '''
1903        self.varLookup = {}
1904        '''Lookup table that specifies the GSAS-II variable(s)
1905        indexed by the expression label name. (Used for only for diagnostics
1906        not evaluation of expression.)
1907        '''
1908        # Patch: for old-style expressions with a (now removed step size)
1909        for v in self.eObj.assgnVars:
1910            if not isinstance(self.eObj.assgnVars[v], basestring):
1911                self.eObj.assgnVars[v] = self.eObj.assgnVars[v][0]
1912
1913    def SetupCalc(self,parmDict):
1914        '''Do all preparations to use the expression for computation.
1915        Adds the free parameter values to the parameter dict (parmDict).
1916        '''
1917        self.fxnpkgdict = self.eObj.CheckVars()
1918        # all is OK, compile the expression
1919        self.compiledExpr = compile(self.eObj.expression,'','eval')
1920
1921        # look at first value in parmDict to determine its type
1922        parmsInList = True
1923        for key in parmDict:
1924            val = parmDict[key]
1925            if isinstance(val, basestring):
1926                parmsInList = False
1927                break
1928            try: # check if values are in lists
1929                val = parmDict[key][0]
1930            except (TypeError,IndexError):
1931                parmsInList = False
1932            break
1933           
1934        # set up the dicts needed to speed computations
1935        self.exprDict = {}
1936        self.lblLookup = {}
1937        self.varLookup = {}
1938        for v in self.eObj.freeVars:
1939            varname = self.eObj.freeVars[v][0]
1940            varname = "::" + varname.lstrip(':').replace(' ','_').replace(':',';')
1941            self.lblLookup[varname] = v
1942            self.varLookup[v] = varname
1943            if parmsInList:
1944                parmDict[varname] = [self.eObj.freeVars[v][1],self.eObj.freeVars[v][2]]
1945            else:
1946                parmDict[varname] = self.eObj.freeVars[v][1]
1947            self.exprDict[v] = self.eObj.freeVars[v][1]
1948        for v in self.eObj.assgnVars:
1949            varname = self.eObj.assgnVars[v]
1950            if '*' in varname:
1951                varlist = LookupWildCard(varname,parmDict.keys())
1952                if len(varlist) == 0:
1953                    raise Exception,"No variables match "+str(v)
1954                for var in varlist:
1955                    self.lblLookup[var] = v
1956                if parmsInList:
1957                    self.exprDict[v] = np.array([parmDict[var][0] for var in varlist])
1958                else:
1959                    self.exprDict[v] = np.array([parmDict[var] for var in varlist])
1960                self.varLookup[v] = [var for var in varlist]
1961            elif varname in parmDict:
1962                self.lblLookup[varname] = v
1963                self.varLookup[v] = varname
1964                if parmsInList:
1965                    self.exprDict[v] = parmDict[varname][0]
1966                else:
1967                    self.exprDict[v] = parmDict[varname]
1968            else:
1969                raise Exception,"No value for variable "+str(v)
1970        self.exprDict.update(self.fxnpkgdict)
1971
1972    def UpdateVars(self,varList,valList):
1973        '''Update the dict for the expression with a set of values
1974        :param list varList: a list of variable names
1975        :param list valList: a list of corresponding values
1976        '''
1977        for var,val in zip(varList,valList):
1978            self.exprDict[self.lblLookup.get(var,'undefined: '+var)] = val
1979
1980    def UpdateDict(self,parmDict):
1981        '''Update the dict for the expression with values in a dict
1982        :param list parmDict: a dict of values some of which may be in use here
1983        '''
1984        for var in parmDict:
1985            if var in self.lblLookup:
1986                self.exprDict[self.lblLookup[var]] = parmDict[var]
1987           
1988    def EvalExpression(self):
1989        '''Evaluate an expression. Note that the expression
1990        and mapping are taken from the :class:`ExpressionObj` expression object
1991        and the parameter values were specified in :meth:`SetupCalc`.
1992        :returns: a single value for the expression. If parameter
1993        values are arrays (for example, from wild-carded variable names),
1994        the sum of the resulting expression is returned.
1995
1996        For example, if the expression is ``'A*B'``,
1997        where A is 2.0 and B maps to ``'1::Afrac:*'``, which evaluates to::
1998
1999        [0.5, 1, 0.5]
2000
2001        then the result will be ``4.0``.
2002        '''
2003        if self.compiledExpr is None:
2004            raise Exception,"EvalExpression called before SetupCalc"
2005        val = eval(self.compiledExpr,globals(),self.exprDict)
2006        if not np.isscalar(val):
2007            val = np.sum(val)
2008        return val
2009
2010
2011if __name__ == "__main__":
2012    # test equation evaluation
2013    def showEQ(calcobj):
2014        print 50*'='
2015        print calcobj.eObj.expression,'=',calcobj.EvalExpression()
2016        for v in sorted(calcobj.varLookup):
2017            print "  ",v,'=',calcobj.exprDict[v],'=',calcobj.varLookup[v]
2018        # print '  Derivatives'
2019        # for v in calcobj.derivStep.keys():
2020        #     print '    d(Expr)/d('+v+') =',calcobj.EvalDeriv(v)
2021
2022    obj = ExpressionObj()
2023
2024    obj.expression = "A*np.exp(B)"
2025    obj.assgnVars =  {'B': '0::Afrac:1'}
2026    obj.freeVars =  {'A': [u'A', 0.5, True]}
2027    #obj.CheckVars()
2028    parmDict2 = {'0::Afrac:0':[0.0,True], '0::Afrac:1': [1.0,False]}
2029    calcobj = ExpressionCalcObj(obj)
2030    calcobj.SetupCalc(parmDict2)
2031    showEQ(calcobj)
2032
2033    obj.expression = "A*np.exp(B)"
2034    obj.assgnVars =  {'B': '0::Afrac:*'}
2035    obj.freeVars =  {'A': [u'Free Prm A', 0.5, True]}
2036    #obj.CheckVars()
2037    parmDict1 = {'0::Afrac:0':1.0, '0::Afrac:1': 1.0}
2038    calcobj = ExpressionCalcObj(obj)
2039    calcobj.SetupCalc(parmDict1)
2040    showEQ(calcobj)
2041
2042    calcobj.SetupCalc(parmDict2)
2043    showEQ(calcobj)
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